Recent questions tagged generating-functions
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Recent questions tagged generating-functions

Recent questions tagged generating-functions
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GATE2016-1-26 Video Solution
The coefficient of $x^{12}$ in $\left(x^{3}+x^{4}+x^{5}+x^{6}+\dots \right)^{3}$ is ___________.
admin asked in Combinatory Apr 18, 2020
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GATE2018-1 Video Solution
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$, where $a_n = 2n +3 \text{ for all } n=0, 1, 2, \dots$? $\frac{3}{(1-x)^2}$ $\frac{3x}{(1-x)^2}$ $\frac{2-x}{(1-x)^2}$ $\frac{3-x}{(1-x)^2}$
admin asked in Combinatory Apr 18, 2020
by admin
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GATE2017-2-47 Video Solution
If the ordinary generating function of a sequence $\left \{a_n\right \}_{n=0}^\infty$ is $\large \frac{1+z}{(1-z)^3}$, then $a_3-a_0$ is equal to ___________ .
admin asked in Combinatory Apr 18, 2020
by admin
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GATE1987-10b Video Solution
What is the generating function $G(z)$ for the sequence of Fibonacci numbers?
admin asked in Combinatory Apr 18, 2020
by admin
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GATE2005-50 Video Solution
Let $G(x) = \frac{1}{(1-x)^2} = \sum\limits_{i=0}^\infty g(i)x^i$, where $|x| < 1$. What is $g(i)$? $i$ $i+1$ $2i$ $2^i$
admin asked in Combinatory Apr 18, 2020
by admin
585 points
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